v^2-18v+55=-10

Solution for v^2-18v+55=-10 equation:

v^2-18v+55=-10

We move all terms to the left:

v^2-18v+55-(-10)=0

We add all the numbers together, and all the variables

v^2-18v+65=0

a = 1; b = -18; c = +65;
Δ = b2-4ac
Δ = -182-4·1·65
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-8}{2*1}=\frac{10}{2}
=5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+8}{2*1}=\frac{26}{2}
=13
$